{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7OR6E2GQI3276W2H24UNLPCOD5","short_pith_number":"pith:7OR6E2GQ","schema_version":"1.0","canonical_sha256":"fba3e268d046f5ff5b47d728d5bc4e1f4f08f5a61b9e433c9c852774370eed37","source":{"kind":"arxiv","id":"1308.0835","version":2},"attestation_state":"computed","paper":{"title":"On the Construction of Simply Connected Solvable Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mark E. Fels","submitted_at":"2013-08-04T18:37:22Z","abstract_excerpt":"Let $\\omega_\\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \\omega_\\mathfrak{g} + \\frac{1}{2} \\omega_\\mathfrak{g}\\wedge \\omega_\\mathfrak{g}=0$ where $\\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $\\rho:M\\to G$, where $G$ is an $n$-dimensional solvable Lie group with Lie algebra $\\mathfrak{g}$ and left invariant Maurer-Cartan form $\\tau$, such that $\\rho^* \\tau= \\omega_\\mathfrak{g}$ can be solved by quadratures and the matrix exponential. In the process we give a closed form formula for the vector "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.0835","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-04T18:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"07dfc93953f65f25c5d5fe5dadf9324600881a4501c291a0fe4b3e37477f7ab8","abstract_canon_sha256":"937262931d85c3ed9e5c7b5b4451d29192bc5f49eaf9330f7f90c92ba5e6e303"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:14.893149Z","signature_b64":"tj6hHR/dJpBuDbybZaHRSnlwvWETWH3sVeAXakjkAri1AKcbScNMWzc3IoDBXg6e7NcLBITDEscpQit5WTdwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fba3e268d046f5ff5b47d728d5bc4e1f4f08f5a61b9e433c9c852774370eed37","last_reissued_at":"2026-05-18T01:24:14.892646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:14.892646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Construction of Simply Connected Solvable Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mark E. Fels","submitted_at":"2013-08-04T18:37:22Z","abstract_excerpt":"Let $\\omega_\\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \\omega_\\mathfrak{g} + \\frac{1}{2} \\omega_\\mathfrak{g}\\wedge \\omega_\\mathfrak{g}=0$ where $\\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $\\rho:M\\to G$, where $G$ is an $n$-dimensional solvable Lie group with Lie algebra $\\mathfrak{g}$ and left invariant Maurer-Cartan form $\\tau$, such that $\\rho^* \\tau= \\omega_\\mathfrak{g}$ can be solved by quadratures and the matrix exponential. In the process we give a closed form formula for the vector "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0835","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.0835","created_at":"2026-05-18T01:24:14.892740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.0835v2","created_at":"2026-05-18T01:24:14.892740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0835","created_at":"2026-05-18T01:24:14.892740+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OR6E2GQI327","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OR6E2GQI3276W2H","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OR6E2GQ","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5","json":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5.json","graph_json":"https://pith.science/api/pith-number/7OR6E2GQI3276W2H24UNLPCOD5/graph.json","events_json":"https://pith.science/api/pith-number/7OR6E2GQI3276W2H24UNLPCOD5/events.json","paper":"https://pith.science/paper/7OR6E2GQ"},"agent_actions":{"view_html":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5","download_json":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5.json","view_paper":"https://pith.science/paper/7OR6E2GQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.0835&json=true","fetch_graph":"https://pith.science/api/pith-number/7OR6E2GQI3276W2H24UNLPCOD5/graph.json","fetch_events":"https://pith.science/api/pith-number/7OR6E2GQI3276W2H24UNLPCOD5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5/action/storage_attestation","attest_author":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5/action/author_attestation","sign_citation":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5/action/citation_signature","submit_replication":"https://pith.science/pith/7OR6E2GQI3276W2H24UNLPCOD5/action/replication_record"}},"created_at":"2026-05-18T01:24:14.892740+00:00","updated_at":"2026-05-18T01:24:14.892740+00:00"}